Question

If the percentage error in the calculation of volume of a cube is $4.5$%, the percentage error in its length is:

• A. $3$%
• B. $2.25$%
• C. $2$%
• D. $1.5$%

Answer 1

Answer: (D)

$1.5$%

$\begin{array}{c}\text{side}=a\\ \text{volume}V=a^3⟶\left(i\right)\\ \text{surface area (S.A)}=6a^2\\ \text{given}\\ \%\text{error in}V\\ =\frac{dV}{V}\times 100=4.5\%\\ \text{differentiating eq.(i)}\end{array}$

$\begin{array}{c}dv=3a^{2}da⟶\left(ii\right)\\ \text{dividing by}V\\ \frac{dV}{V}=\frac{3a^{2}da}{y}\\ \Rightarrow \frac{dV}{V}\times 100=3\frac{a^{2}da}{a^3}\times 100=\frac{3da}{a}\times 100\\ \Rightarrow \frac{da}{a}\times 100=\frac{1}{3}\times 4\cdot 5=1.5\%\end{array}$